000 07620cam a2200805 a 4500
001 ocn624365972
003 OCoLC
005 20220713030747.0
006 m o d
007 cr cuu|||uu|||
008 100520s2010 enka ob 001 0 eng d
040 _aLLB
_beng
_epn
_cLLB
_dN$T
_dOCLCQ
_dCDX
_dOCLCQ
_dYDXCP
_dOCLCF
_dOCLCO
_dOCLCQ
_dAGLDB
_dOCLCQ
_dVTS
_dVT2
_dOCLCQ
_dWYU
_dOCLCO
_dSTF
_dOCLCO
_dJBG
_dLEAUB
_dM8D
_dAJS
_dOCLCO
_dOCLCQ
016 7 _a015369161
_2Uk
019 _a666256886
_a670430586
_a1055403219
_a1063812033
_a1086435527
020 _a9781848164468
_q(electronic bk.)
020 _a1848164467
_q(electronic bk.)
020 _a9786612760006
020 _a6612760001
020 _z1848164459
020 _z9781848164451
024 8 _a9786612760006
029 1 _aAU@
_b000051395989
029 1 _aDEBBG
_bBV043138384
029 1 _aDEBSZ
_b421675705
029 1 _aGBVCP
_b803174098
035 _a(OCoLC)624365972
_z(OCoLC)666256886
_z(OCoLC)670430586
_z(OCoLC)1055403219
_z(OCoLC)1063812033
_z(OCoLC)1086435527
037 _a276000
_bMIL
050 4 _aQA402.5
_b.L37 2010eb
072 7 _aMAT
_x042000
_2bisacsh
082 0 4 _a519.6
_222
049 _aMAIN
100 1 _aLasserre, Jean-Bernard,
_d1953-
_9381471
245 1 0 _aMoments, positive polynomials and their applications /
_cJean Bernard Lasserre.
260 _aLondon :
_bImperial College Press ;
_aSingapore :
_bDistributed by World Scientific Pub. Co.,
_c©2010.
300 _a1 online resource (xxi, 361 pages) :
_billustrations (some color).
336 _atext
_btxt
_2rdacontent
337 _acomputer
_bc
_2rdamedia
338 _aonline resource
_bcr
_2rdacarrier
490 1 _aImperial College Press optimization series,
_x2041-1677 ;
_vv. 1
504 _aIncludes bibliographical references (pages 341-358) and index.
505 0 _a1. The generalized moment problem. 1.1. Formulations. 1.2. Duality theory. 1.3. Computational complexity. 1.4. Summary. 1.5. Exercises. 1.6. Notes and sources -- 2. Positive polynomials. 2.1. Sum of squares representations and semi-definite optimization. 2.2. Nonnegative versus s.o.s. polynomials. 2.3. Representation theorems : univariate case. 2.4. Representation theorems : mutivariate case. 2.5. Polynomials positive on a compact basic semi-algebraic set. 2.6. Polynomials nonnegative on real varieties. 2.7. Representations with sparsity properties. 2.8. Representation of convex polynomials. 2.9. Summary. 2.10. Exercises. 2.11. Notes and sources -- 3. Moments. 3.1. The one-dimensional moment problem. 3.2. The multi-dimensional moment problem. 3.3. The K-moment problem. 3.4. Moment conditions for bounded density. 3.5. Summary. 3.6. Exercises. 3.7. Notes and sources -- 4. Algorithms for moment problems. 4.1. The overall approach. 4.2. Semidefinite relaxations. 4.3. Extraction of solutions. 4.4. Linear relaxations. 4.5. Extensions. 4.6. Exploiting sparsity. 4.7. Summary. 4.8. Exercises. 4.9. Notes and sources. 4.10. Proofs -- 5. Global optimization over polynomials. 5.1. The primal and dual perspectives. 5.2. Unconstrained polynomial optimization. 5.3. Constrained polynomial optimization : semidefinite relaxations. 5.4. Linear programming relaxations. 5.5. Global optimality conditions. 5.6. Convex polynomial programs. 5.7. Discrete optimization. 5.8. Global minimization of a rational function. 5.9. Exploiting symmetry. 5.10. Summary. 5.11. Exercises. 5.12. Notes and sources -- 6. Systems of polynomial equations. 6.1. Introduction. 6.2. Finding a real solution to systems of polynomial equations. 6.3. Finding all complex and/or all real solutions : a unified treatment. 6.4. Summary. 6.5. Exercises. 6.6. Notes and sources -- 7. Applications in probability. 7.1. Upper bounds on measures with moment conditions. 7.2. Measuring basic semi-algebraic sets. 7.3. Measures with given marginals. 7.4. Summary. 7.5. Exercises. 7.6. Notes and sources -- 8. Markov chains applications. 8.1. Bounds on invariant measures. 8.2. Evaluation of ergodic criteria. 8.3. Summary. 8.4. Exercises. 8.5. Notes and sources -- 9. Application in mathematical finance. 9.1. Option pricing with moment information. 9.2. Option pricing with a dynamic model. 9.3. Summary. 9.4. Notes and sources -- 10. Application in control. 10.1. Introduction. 10.2. Weak formulation of optimal control problems. 10.3. Semidefinite relaxations for the OCP. 10.4. Summary. 10.5. Notes and sources -- 11. Convex envelope and representation of convex sets. 11.1. The convex envelope of a rational function. 11.2. Semidefinite representation of convex sets. 11.3. Algebraic certificates of convexity. 11.4. Summary. 11.5. Exercises. 11.6. Notes and sources -- 12. Multivariate integration 12.1. Integration of a rational function. 12.2. Integration of exponentials of polynomials. 12.3. Maximum entropy estimation. 12.4. Summary. 12.5. Exercises. 12.6. Notes and sources -- 13. Min-max problems and Nash equilibria. 13.1. Robust polynomial optimization. 13.2. Minimizing the sup of finitely many rational cunctions. 13.3. Application to Nash equilibria. 13.4. Exercises. 13.5. Notes and sources -- 14. Bounds on linear PDE. 14.1. Linear partial differential equations. 14.2. Notes and sources.
520 _aMany important applications in global optimization, algebra, probability and statistics, applied mathematics, control theory, financial mathematics, inverse problems, etc. can be modeled as a particular instance of the Generalized Moment Problem (GMP). This book introduces a new general methodology to solve the GMP when its data are polynomials and basic semi-algebraic sets. This methodology combines semidefinite programming with recent results from real algebraic geometry to provide a hierarchy of semidefinite relaxations converging to the desired optimal value. Applied on appropriate cones, standard duality in convex optimization nicely expresses the duality between moments and positive polynomials. In the second part, the methodology is particularized and described in detail for various applications, including global optimization, probability, optimal control, mathematical finance, multivariate integration, etc., and examples are provided for each particular application.
588 0 _aPrint version record.
590 _aeBooks on EBSCOhost
_bEBSCO eBook Subscription Academic Collection - Worldwide
650 0 _aMathematical optimization.
650 0 _aMoment problems (Mathematics)
_9226483
650 0 _aGeometry, Algebraic.
_9101299
650 0 _aPolynomials.
_9128196
650 6 _aOptimisation mathématique.
_9878326
650 6 _aProblèmes des moments (Mathématiques)
_91463471
650 6 _aGéométrie algébrique.
_9894815
650 6 _aPolynômes.
_9951770
650 7 _aMATHEMATICS
_xOptimization.
_2bisacsh
_9924403
650 7 _aGeometry, Algebraic.
_2fast
_0(OCoLC)fst00940902
_9101299
650 7 _aMathematical optimization.
_2fast
_0(OCoLC)fst01012099
650 7 _aMoment problems (Mathematics)
_2fast
_0(OCoLC)fst01025012
_9226483
650 7 _aPolynomials.
_2fast
_0(OCoLC)fst01070715
_9128196
650 7 _aPositives Polynom
_2gnd
_91463472
655 0 _aElectronic book.
655 4 _aElectronic book.
710 2 _aWorld Scientific (Firm)
_974845
776 1 _z1848164459
776 1 _z9781848164451
830 0 _aImperial College Press optimization series ;
_vv. 1.
_9340731
856 4 0 _uhttps://search.ebscohost.com/login.aspx?direct=true&scope=site&db=nlebk&AN=340588
938 _aCoutts Information Services
_bCOUT
_n15220667
938 _aEBSCOhost
_bEBSC
_n340588
938 _aYBP Library Services
_bYANK
_n3511269
994 _a92
_bINOPJ
999 _c2922540
_d2922540